The Euler Number as an Index of Spatial Integrity of Landscapes: Evaluation and Proposed Improvement |
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Authors: | JAN BOGAERT PIET VAN HECKE REINHART CEULEMANS |
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Affiliation: | (1) University of Antwerp (UIA), Department of Biology, Research Group of Plant and Vegetation Ecology, Universiteitsplein 1, B-2610 Wilrijk, Belgium, BE |
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Abstract: | The spatial integrity of a habitat or landscape is determined by the occurrence of habitat fragments and of perforations inside them. A landscape is said to have less spatial integrity with increasing numbers of fragments and perforations. The Euler number (ε) is a numerical measure of spatial integrity, based upon the difference |n f −n p | between the number of fragments (n f ) and the number of perforations (n p ). In this contribution, ε is evaluated, and an improvement is presented as a new index ε*, which is a combination of two metrics (ε i , ε d ) based on n f and n p . The term ε i quantifies the intensity of perforation and/or fragmentation. The term ε d measures the extent to which fragmentation predominates perforation, and vice versa. The intensity and dominance measures are combined into an Euclidean distance measure, generating the new ensemble value ε*, calculated as ε*= (n f +n p )−1√[1 +n f 2]. Use, sensitivity, and application of ε*, ε i , and ε d are illustrated using percolation maps. Application of the new metrics by environmental scientists is encouraged because (1) no negative values can be generated with ε*, ε i , and ε d ; (2) the range of ε*, ε i , and ε d is fixed; (3) process dominance and intensity are both assessed; (4) ε*, ε i , and ε d are easy to calculate and to interpret; and (5) ε* is not only based upon |n f −n p |, as ε is. Guidelines for practical use by means of a biplot of ε i and ε d are given. |
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Keywords: | : Euler number Fragmentation Landscape ecology Percolation theory Perforation Spatial integrity |
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